Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on $\mathbb{R}^{d+1}$ (Analysis in Theory and Applications, 2023)
In this paper we consider the Heckman-Opdam-Jacobi operator $∆_{HJ}$ on $\mathbb{R}^{d+1}.$ We define the Heckman-Opdam-Jacobi intertwining operator $V_{HJ},$ which turns out tobe the transmutation operator between $∆_{HJ}$ and the Laplacian $∆_{d+1}.$ Next we construct $^tV_{HJ}$ the dual of this intertwining operator. We exploit these operators to develop anew harmonic analysis corresponding to $∆_{HJ}.$
Keywords: Heckman-Opdam-Jacobi operator; generalized intertwining operator and its dual; generalized Fourier transform; generalized translation operators.